The Analysis of Arithmetic

Patricia A. Blanchette

in Frege’s Conception of Logic

Published in print April 2012 | ISBN: 9780199891610
Published online May 2012 | e-ISBN: 9780199933211 | DOI:
The Analysis of Arithmetic

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This chapter treats the question of how Frege understands the connection between the familiar truths of ordinary arithmetic and the unfamiliar and complex truths with which his formal proofs conclude. It is argued that although Frege does not intend ordinary and formal sentences to express the same thoughts or to be “about” the same objects, nevertheless the relationship between the two kinds of sentence is intended to be sufficiently close that the success of the project would, in fact, have demonstrated the purely-logical status of ordinary arithmetic. It is argued, as against Joan Weiner, that the semantic distance between ordinary and derived sentences does not undermine this straightforward reading of Frege’s project.

Keywords: arithmetic; analysis; reference-preservation; reduction; proof

Chapter.  14537 words. 

Subjects: Philosophy of Mathematics and Logic

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